Systems for measuring electric resistance and relation between applied pressure and streaming potential across the membrane and utility thereof

ABSTRACT

The present invention provides a method for measuring net charge density of membrane and apparatus thereof. The method measures the net charge density of a membrane by utilizing the relation between the mechanical pressure difference applied across the membrane and the generated streaming potential or the relation between the applied electric field and the generated electroosmotic flow. The present invention also provides a method and an apparatus for measuring the resistance of a membrane.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a divisional of U.S. Ser. No. 13/193,982, filed Jul. 29, 2011 bythe same inventors, and claims priority there from. This divisionalapplication contains rewritten claims to the restricted-out subjectmatter of original claims.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is generally related to a method for measuring anet charge density of a membrane and an apparatus thereof, and moreparticularly to a method for measuring a net charge density of a porousmembrane such as a microfiltration, ultrafiltration or nanofiltrationmembrane and an apparatus thereof.

2. Description of the Prior Art

The characteristic parameters of a membrane generally can be categorizedinto performance parameters, morphology parameter, and chargeparameters. In the charge parameters, the zeta potential of a membraneusually is measured by the streaming potential method or electroosmosismethod and its influence to the filtration performance of the membraneis analyzed but the net charge density inside the membrane is usuallyuncertain.

Particularly, regarding nanofiltration (NF) membranes, the key of thespecies rejection mechanism of a nanofiltration (NF) membrane is theelectrostatic repulsion between species and the NF membrane. Theelectrostatic repulsion force is an important factor in controlling thefiltration performance. The charge parameters used to evaluate thefiltration performance of the NF membrane and the ion exchange membraneare usually estimated from the net charge density per unit volume orarea of a membrane. According to the prior art, the value of the netcharge density of a NF membrane per unit volume is usually acquired bythe estimation from the experimental result accompanying with thetheoretical simulation. Since most of the NF membranes are compositemembranes, the pore diameter is very small and thus overlapping ofelectric double layers is very serious to thereby cause the difficultyin measuring the real zeta potential of the surfaces of the pore wallsof the NF membrane.

Regarding the estimation of the net charge density per unit volume,Ta-Shung et al. (Tai-Shung, C., J. Lv and W. Kai Yu, “Investigation ofamphoteric polybenzimidazole (PBI) nanofiltration hollow fiber membranefor both cation and anions removal”, J. Membrane Sci., 310, 557-566(2008)) use Speigler-Kedem model (SKM) together withTeorell-Meyer-Sievers model (TMS) to estimate the net charge density perunit volume for PBI nanofiltration (NF) membrane. SKM is used todescribe the relation between solution flux and solute flux while TMS isused to describe the relation of ion permeation. Such a methodaccompanying with the result of the experimental blocking ratecalculates the reflection coefficient of the membrane to therebyestimate the charge quantity of the membrane per unit volume. The resultindicates that the effective net charge density per unit volume of themembrane increases with the increase of the ionic concentration.

On the other hand, Bandini et al. (Bandini, S., D. Jennifer and V.Daniele, “The role of pH and concentration on the ion rejection inpolyamide nanofiltration membranes”, J. Membrane Sci., 264, 65-74(2005)) use DSPM-DE (Donnan Steric Pore Model (DSPM) and DielectricExclusion) to estimate the net charge density per unit volume for theDK02 nanofiltration (NF) membrane (OSMONICS). The experiment offiltration of a sodium chloride aqueous solution is performed and theblocking rate obtained from the experiment accompanying with thetheoretical model and the charge neutrality balance condition is used toestimate the net charge density per unit volume. The result shows thatthe charge density increases with the increase of the concentration ofsalts. The same result is obtained even for different pH values. Then,Bandini et al. (Bandini, S. and C. Mazzoni, “On nanofiltration Desal-5DK performances with calcium chloride-water solutions”, Separation andPurification Technology, 52, 232-240 (2006)) also use DK02nanofiltration (NF) membranes in the CaCl₂ circulating sweepingfiltration experiment and then the volumetric net charge density of theNF membrane is estimated from the ion blocking experimental result. Theestimation result indicates that the electrical potential of themembrane is increased by ion adsorption and due to the competitionbetween the adsorption of calcium ions and the adsorption of chlorideions when the concentration is increased to a threshold level theisoelectric point of volumetric charges of the membrane appears at twodifferent concentrations.

Therefore, when, according to the prior art, the method of utilizing theexperimental result of the ion blocking rate together with thetheoretical model is applied to simulate the net charge density, thecharge density is increased with the increase of the concentration ofions. In addition, it is found that larger deviation in estimation willappear if different methods are used based on various ionic radiidefined. Thus, it is important to effectively measure a net chargedensity per unit volume and a more reliable measurement method isrequired.

SUMMARY OF THE INVENTION

In light of the above background, in order to fulfill the industrialrequirements, the invention provides a method for measuring a net chargedensity of a membrane and an apparatus thereof.

One object of the present invention is to provide a method for measuringa net charge density of a membrane and an apparatus thereof to measurethe net charge density of a porous membrane such as a microfiltration(MF), ultrafiltration (UF) or nanofiltration (NF) membrane.

One object of the present invention is to provide a method for measuringa net charge density of a membrane and an apparatus thereof to utilizethe equilibrium condition between the applied mechanical pressuredifference and the electroosmotic flow of the membrane to acquire thenet charge density of the membrane per unit volume.

One object of the present invention is to provide a method for measuringa net charge density of a membrane and an apparatus thereof to use therelation of the applied mechanical pressure difference and the streamingpotential of the membrane to acquire the net charge density per unitvolume of the membrane.

One object of the present invention is to provide a method for measuringelectric resistance of a membrane and an apparatus thereof to measurethe resistance of a porous membrane such as a microfiltration (MF),ultrafiltration (UF) or nanofiltration (NF) membrane. Furthermore, ifthe porosity of the membrane is known to be ∈ (for example, when amembrane has large pores, the porosity ∈ can be obtained from othermethods), the average electrical conductivity k_(m) of the membrane canbe acquired according to the method and apparatus for measuring electricresistance of a membrane disclosed by the invention. On the other hand,if the average electrical conductivity k_(m) of the membrane is known,the porosity ∈ can be acquired according to the method and apparatus formeasuring electric resistance of a membrane disclosed by the invention.

Accordingly, one embodiment of the invention provides a method formeasuring a net charge density of a membrane. The method comprises thefollowing steps. At first, a membrane to be measured is provided. Asolution is provided and infiltrates the membrane. Then, a mechanicalpressure difference ΔP is applied across the membrane to generatepermeate flow as well as streaming potential. The net charge densityρ_(E) of the membrane per unit volume is acquired according to therelation of the mechanical pressure difference ΔP and the streamingpotential Ē by the following equation (7): ρ_(E)=−(Ē/ΔP)*(μ∈k_(m)/K_(p))where ∈k_(m) represents the product of the porosity ∈ and averageelectrical conductivity k_(m) of the membrane, μ represents viscosity ofthe solution, and K_(p) represents permeability. Or, after applying amechanical pressure difference ΔP, an electric field is applied acrossthe membrane to generate osmotic flow. The net charge density ρ_(E) ofthe membrane per unit volume is then calculated according to therelation between the electric field E and the mechanical pressuredifference ΔP or between the osmotic flow and the current applied.

In one embodiment, in the above method, ρ_(E) represents the net chargedensity of the membrane per unit volume can be acquired by the followingequation (9): ρ_(E)=−(Q_(p)/I_(a))*(μ∈k_(m)/K_(p)) where ∈k_(m)represents the product of the porosity ∈ and average electricalconductivity k_(m) of the membrane, μ represents viscosity of thesolution, K_(p) represents permeability obtained from the permeate flow,I_(a) represents the current induced by the electric field, and Q_(p)represents the electroosmotic volumetric flow rate of the osmotic flow.On the other hand, when a mechanical pressure difference ΔP is appliedto generate the first permeate flow, the streaming potential Ē betweenthe two surfaces of the membrane is measured at the same time. The netcharge density ρ_(E) of the membrane per unit volume can be acquired bythe equation (7): ρ_(E)=−(Ē/ΔP)*(μ∈k_(m)/K_(p)).

In one embodiment, in the above method, the product of the porosity ∈and average electrical conductivity k_(m) of the membrane is acquired bymeasuring electric resistance of the membrane.

In one embodiment, the method of measuring electric resistance of themembrane comprises: providing a solution; having the solution infiltratethe membrane; disposing the membrane between two electrodes and fillingthe solution between the membrane and each electrode; and measuring therelation of current and voltage between the two electrodes while thetarget membrane is installed in between or is not installed andcalculating the resistance of the membrane according to Ohm's law.

In one embodiment, in the above method, the membrane to be measured isselected from the group consisting of the following: porous membrane,microfiltration membrane, ultrafiltration membrane, nanofiltrationmembrane, and ion exchange membrane.

In one embodiment, in the above method, a predetermined mechanicalpressure difference is used to generate permeate flow and the electricfield strength is adjusted to have the electroosmotic flow be equal tothe permeate flow in magnitude but be opposite in direction. That is,the electric field strength is adjusted to have the first permeate flowgenerated by the mechanical pressure difference stop to therebycalculate the net charge density ρ_(E) of the membrane per unit volume.In the above method, on the other hand, the mechanical pressuredifference ΔP is applied and the streaming potential Ē between the twosurfaces of the membrane is measured at the same time so that thestreaming potential coefficient (Ē/ΔP) can be used to calculate the netcharge density ρ_(E).

In one embodiment, the membrane to be measured is a porous membraneincluding microfiltration membrane, ultrafiltration membrane,nanofiltration membrane, or ion exchange membrane.

In one embodiment, the method for measuring the streaming potential usesa high impedance voltmeter to measure the potential difference acrossthe membrane.

Another embodiment of the invention provides an apparatus for measuringa net charge density of a membrane, comprising: a membrane permeationmeasurement module, a pressure measurement module, and a streamingpotential measurement module. The membrane permeation measurement modulecomprises a chamber, two electrodes disposed in the chamber, a membraneto be measured, and a liquid, for measuring permeation rate caused by amechanical pressure difference between two surfaces of the membrane andelectroosmotic volumetric flow rate caused by an electric field applyingon the two surfaces of the membrane. The pressure measurement modulemeasures the mechanical pressure difference between the two surfaces ofthe membrane. The streaming potential measurement module measures thestreaming potential of the membrane.

In one embodiment, the apparatus further comprises a membrane electricresistance measurement module, for measuring electric resistance of themembrane.

In one embodiment, the membrane permeation measurement module furthercomprises: a temperature controller, for controlling the chamber at afixed temperature; a pump, for transporting the solution into thechamber; an electronic balance, for measuring a flow quantity of theliquid flowing through the membrane and outputting the flow quantity;and a power supply, electrically coupled to the two electrodes of themembrane permeation measurement module.

In one embodiment, the pressure measurement module comprises: a pressurevalve, for controlling and applying a pressure on the two surfaces ofthe membrane to generate a mechanical pressure difference ΔP across themembrane; and a pressure sensor, for measuring the mechanical pressuredifference ΔP and outputting the mechanical pressure difference ΔP.

In one embodiment, the streaming potential measurement module comprises:a high impedance voltmeter, for measuring voltage between the twoelectrodes when the liquid passes through the membrane and outputtingthe voltage.

In one embodiment, the membrane electric resistance measurement modulecomprises: a membrane resistance measurement container; twoplate-electrodes, disposed in the membrane resistance measurementcontainer and having a specific distance between the two electrodeplates; a solution, filled in the membrane resistance measurementcontainer; an AC power supply, for supplying power between the twoelectrode plates; two voltmeter, one of which is electrically coupled tothe two electrode plates and the other of which has one end electricallycoupled to the AC power supply and has the other end electricallycoupled to one of the two electrode plates to measure voltages andcurrents; wherein under a specific voltage the variation of currentsbetween the two electrodes is measured while the membrane is installedin between or is not installed and then the electric resistance of themembrane is calculated from the above relation of current variationbased on Ohm's law.

Another embodiment of the invention provides an apparatus for measuringelectric resistance of a membrane by having the above membraneresistance measurement module become a stand-alone apparatus.

Another embodiment of the invention provides a method for measuringelectric resistance of a membrane, comprising: providing a solution;having the solution infiltrate the membrane; disposing the membranebetween two electrodes and filling the solution between the membrane andeach electrode; and measuring the relation of current and voltagebetween the two electrodes while the membrane is installed in between oris not installed and calculating the electric resistance of the membraneaccording to Ohm's law.

In conclusion, the present invention discloses a method for measuring anet charge density of a membrane and the apparatus thereof to utilizethe applied mechanical pressure difference and the streaming potentialof the membrane or the applied electric field and the electroosmoticvolumetric flow rate of the electroosmotic flow to acquire the netcharge density inside the membrane so that the net charge density perunit volume can be measured effectively to solve the problem in theprior art.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic diagram illustrating a membrane being soaked ina solution and applied with a mechanic pressure and an electric fieldaccording to one embodiment of the invention;

FIG. 2 shows a schematic diagram illustrating a membrane electricresistance measurement module according to one embodiment of theinvention;

FIG. 3 shows a functional block diagram illustrating an apparatus formeasuring a net charge density of a membrane according to one embodimentof the invention;

FIG. 4 shows a functional block diagram illustrating an apparatus formeasuring a net charge density of a membrane according to anotherembodiment of the invention;

FIG. 5 shows a schematic diagram illustrating the connection of themembrane permeation measurement module 200, the pressure measurementmodule 300, and the streaming potential measurement module 400 shown inFIG. 3;

FIG. 6 shows a schematic diagram illustrating the connection of themembrane permeation measurement module 200, the pressure measurementmodule 300, the streaming potential measurement module 400 and theelectroosmotic flow measurement module 450 shown in FIG. 4; and

FIG. 7 shows a schematic diagram illustrating a membrane electricresistance measurement module 500 according to one embodiment of theinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention discloses a method for measuring a net charge density of amembrane and the apparatus thereof as well as a method and an apparatusfor measuring electric resistance of a membrane. Detail descriptions ofthe steps and elements will be provided in the following in order tomake the invention thoroughly understood. Obviously, the application ofthe invention is not confined to specific details familiar to those whoare skilled in the art. On the other hand, the common steps and elementsthat are known to everyone are not described in details to avoidunnecessary limits of the invention. Some preferred embodiments of thepresent invention will now be described in greater detail in thefollowing. However, it should be recognized that the present inventioncan be practiced in a wide range of other embodiments besides thoseexplicitly described, that is, this invention can also be appliedextensively to other embodiments, and the scope of the present inventionis expressly not limited except as specified in the accompanying claims.

The method for measuring a net charge density of a membrane of thepresent invention utilizes the balance condition of the appliedmechanical pressure difference and the electroosmotic flow or therelation of the applied mechanical pressure difference and the streamingpotential to obtain the net charge density of a membrane per unitvolume. The so called “balance condition of the applied mechanicalpressure difference and the electroosmotic flow” means that for the poreof the membrane in a solution experience an electric force and amechanical pressure where the electric force is equal to mechanicalpressure. That is, a mechanical pressure difference ΔP is applied on thetwo sides (two surfaces) of the membrane to generate permeate flow andthen an electric field is applied to generate electroosmotic flow tohave the magnitude equal to the permeate flow but opposite in directionso that the net charge density of the membrane can be obtained from therelation of the electric field and the mechanical pressure differenceΔP. Or, the mechanical pressure difference ΔP and the electric field canbe applied separately and the condition of the magnitude of permeatedflow by the mechanical pressure difference ΔP is the same as theelectroosmotic flow induced by an electric field is then selected toacquire the net charge density of the membrane. FIG. 1 shows a schematicdiagram illustrating a membrane being soaked in a solution and appliedwith a mechanical pressure and an electric field according to oneembodiment of the invention where E represents the applied electricfield, L represents the thickness of the membrane, ΔP represents theapplied mechanical pressure difference, Q_(p) represents theelectroosmotic volumetric flow rate of the electroosmotic flow, and υrepresents the superficial velocity.

Specifically, assuming the thickness (L), porosity (∈), andcross-sectional area (A) of a membrane are known, as shown in FIG. 1,when DC (direct current) electric field strength (E) is applied acrossthe membrane, the solution in the pores of the membrane experiences aforce caused by the electric field, shown by the following equation (1):F _(e)=ρ′_(E) ×A×L×∈×E  (1)

where ρ′_(E) is the net charge of the solution per unit volume in thepores and the net charge density ρ_(E) of the membrane per unit volumecan be represented by ρ_(E)=−ρ′_(E) based on the assumption ofelectrical neutrality of the whole membrane.

If a mechanical pressure difference is applied on the two surfaces ofthe membrane instead, the solution in the pores of the membraneexperiences a force caused by the mechanical pressure difference, shownby the following equation (2):F _(P) =ΔP×A×∈  (2)

where ΔP represents the applied mechanical pressure difference.

An electric field is applied to generate electroosmotic flow of thesolution in the pores while a mechanical pressure difference is appliedto generate permeate flow. When the electroosmotic flow is equal to thepermeate flow, that is, the two forces are the same (equation(1)=equation (2)), the following equation (3) is obtained:

$\begin{matrix}{\frac{\Delta\; P}{L} = {\rho_{E}^{\prime} \times {E.}}} & (3)\end{matrix}$

A liquid flowing in a porous body can be represented by Darcy's law,shown in the following equation (4):

$\begin{matrix}{\frac{\Delta\; P}{L} = \frac{\mu\upsilon}{K_{P}}} & (4)\end{matrix}$

where K_(p) represents permeability and u represents the superficialvelocity.

The following equation (5) can be obtained from the equations (3) and(4):

$\begin{matrix}{\rho_{E}^{\prime} = \frac{\mu\upsilon}{K_{P}E}} & (5)\end{matrix}$

Besides, by using the relation of the electric field strength and thecurrent, that is, the equation (6):

$\begin{matrix}{E = \frac{I}{k_{m}A\; ɛ}} & (6)\end{matrix}$

the following equation (7) can be obtained:

$\begin{matrix}{\rho_{E}^{\prime} = {\frac{\mu\; k_{m}ɛ}{K_{P}}\left( \frac{Q_{P}}{I_{a}} \right)}} & (7)\end{matrix}$

where k_(m) represents the average electrical conductivity of thesolution in the porous body, Q_(p) represents the electroosmoticvolumetric flow rate (=υA), and I_(a) represents the electric current.

Then, according to Onsager principle, the relation of the electroosmoticflow and the streaming potential Ē is shown by the following equation(8):

$\begin{matrix}{\frac{\overset{\_}{E}}{\Delta\; P} = {\frac{Q_{P}}{I}.}} & (8)\end{matrix}$

Therefore, the net charge of the solution per unit volume in the poresρ′_(E) can be represented by the following equation (9):

$\begin{matrix}{\rho_{E}^{\prime} = {\frac{\mu\; k_{m}ɛ}{K_{P}}\left( \frac{\overset{\_}{E}}{\Delta\; P} \right)}} & (9)\end{matrix}$

where Ē represents the streaming potential and ΔP represents the appliedmechanical pressure difference. According to the method of theinvention, base on the equation (7), the relation of the measuredelectroosmotic volumetric flow rate of the membrane and the appliedcurrent can be used to acquire the net charge density. Besides, based onthe equation (9), the relation of the measured streaming potential andthe mechanical pressure difference can be used to acquire the net chargedensity.

In the above equations (7) and (9), the average electrical conductivityk_(m) of the solution in the pores should be obtained while the netcharge density is to be determined. Since the overlapping of electricdouble layers becomes obvious accompanying with the decrease of the porediameter of the membrane, there is serious deviation if the conductivityk_(b) of the bulk solution is used to estimate the net charge density.Thus, the method for measuring a net charge density of a membrane of thepresent invention also provides a method for measuring electricresistance of the membrane and the conductivity of the solution in thepores is obtained from the data of the electric resistance of themembrane.

FIG. 2 shows a schematic diagram illustrating a membrane electricresistance measurement module. The membrane to be measured is soaked inthe solution and a voltage is applied between the two electrodes. Thesum of the resistance R_(s) of the solution and the resistance R_(m) ofthe membrane is R₁, that is, R₁=R_(s)+R_(m). If the membrane material isnon-electrically-conductive, when the thickness of the membrane is L,the cross-sectional area is A, the porosity is ∈, the relation of R_(m)and the average conductivity k_(m) of the solution in the pores is

$R_{m} = {\frac{L}{A\; ɛ\; k_{m}}.}$The following equation (10) can be obtained when

$R_{m} = \frac{L}{A\; ɛ\; k_{m}}$is inserted into the equation of R₁:

$\begin{matrix}{R_{1} = {R_{s} + {\frac{L}{A\; ɛ\; k_{m}}.}}} & (10)\end{matrix}$

In the same module, after the membrane is taken out, the resistance R₂is measured and the following equation (11) is obtained:

$\begin{matrix}{R_{2} = {R_{s} + \frac{L}{{Ak}_{b}}}} & (11)\end{matrix}$

where k_(b) represents the conductivity of the bulk solution contactingthe membrane surface. The resistance difference ΔR (=R₁−R₂) with orwithout the membrane in the solution is obtained from subtracting R₂from R₁ and then the following equation (12) is obtained byrearrangement:

$\begin{matrix}{\frac{k_{b}}{ɛ\; k_{m}} = {1 + {\frac{{Ak}_{b}\Delta\; R}{L}.}}} & (12)\end{matrix}$

For micro-pores, unless the ionic strength of the solution is very high,k_(b) is not equal to k_(m) (k_(b)≠k_(m)). The above equation (12) canbe used to acquire the product (∈k_(m)) of the porosity ∈ and averageelectrical conductivity k_(m) of the membrane.

According to one embodiment of the invention, the method for measuring anet charge density of a membrane is disclosed. The method comprises thefollowing steps. At first, a membrane to be measured is provided wherethe product (∈k_(m)) of the porosity E and average electricalconductivity k_(m) of the membrane is known and can be obtained from theabove equation (12) by the apparatus shown in FIG. 2. A solution isprovided and infiltrates the membrane. Then, a mechanical pressuredifference ΔP is applied between two surfaces of the membrane(substantially the two ends of the pore in the membrane) to generatepermeate flow. After applying a mechanical pressure difference ΔP, anelectric field is applied on the two surfaces of the membrane togenerate electroosmotic flow. The net charge density ρ_(E) of themembrane per unit volume is then acquired according to the relationbetween the electric field E and the mechanical pressure difference ΔPor between the electroosmotic flow and the current when the permeateflow is equal to the electroosmotic flow. That is, the net chargedensity ρ_(E) of the membrane per unit volume can be calculated by thefollowing equation (9): ρ_(E)=−(Q_(p)/I_(a))*(μ∈k_(m)/K_(p)) where∈k_(m) represents the product of the porosity ∈ and average electricalconductivity k_(m) of the membrane, μ represents viscosity of thesolution, K_(p) represents permeability obtained from the permeate flow,I_(a) represents the current caused by the electric field, and Q_(p)represents the volumetric flow rate of the electroosmotic flow.

In the above method, the procedure of applying the mechanical pressuredifference and the procedure of applying the electric field can beperformed separately to measure the permeate flow at differentmechanical pressure differences and the electroosmotic flow at differentelectric field strength separately. From the permeate flows and theelectroosmotic flows generated by the two procedures respectively, themechanical pressure difference ΔP and the electric field E at the timethe permeate flow is equal to the electroosmotic flow are selected tocalculate the net charge density ρ_(E) of the membrane per unit volume.On the other hand, the procedure of applying the mechanical pressuredifference and the procedure of applying the electric field can beperformed at the same time. A predetermined mechanical pressuredifference is used to generate permeate flow and the electric fieldstrength is adjusted to have the electroosmotic flow be equal to thepermeate flow in magnitude but opposite in direction. That is, theelectric field strength is adjusted to have the permeate flow generatedby the mechanical pressure difference stop and then the mechanicalpressure difference ΔP and the electric field E at the time are used toobtain the net charge density ρ_(E) of the membrane per unit volume.

According to another embodiment of the invention, the method formeasuring a net charge density of a membrane is disclosed. The methodcomprises the following steps. At first, a membrane to be measured isprovided where the product (∈k_(m)) of the porosity E and averageelectrical conductivity k_(m) of the membrane is known and can beobtained from the above equation (12) by the apparatus shown in FIG. 2.A solution is provided and infiltrates the membrane. Then, a mechanicalpressure difference ΔP is applied between two surfaces of the membrane(substantially the two ends of the pore in the membrane) to generatepermeate flow as well as streaming potential. The net charge densityρ_(E) of the membrane per unit volume is calculated according to therelation of the mechanical pressure difference ΔP and the streamingpotential Ē by the following equation (7): ρ_(E)=−(Ē/ΔP)*(μ∈k_(m)/K_(p))where ∈k_(m) represents the product of the porosity ∈ and averageelectrical conductivity k_(m) of solution in the membrane pore, μrepresents viscosity of the solution, and K_(p) represents permeability.

In one embodiment, the method for measuring the resistance of themembrane uses the above module (or apparatus) shown in FIG. 2. Theelectric resistance of the membrane can be obtained from the followingsteps and the equation (12) is used to obtain the product (∈k_(m)). Atfirst, a solution is provided and infiltrates the membrane. The membraneis disposed between two electrodes and the solution is filled betweenthe membrane and each electrode. The relation of current and voltagebetween the two electrodes twice while the target membrane is installedin between and is not installed is measured and the electric resistanceof the membrane is calculated according to Ohm's law.

In one embodiment, the method of having the electroosmotic flow equal tothe permeate flow in magnitude but opposite in direction is to adjustthe electric field strength to have the permeate flow generated by themechanical pressure difference stop. In one embodiment, the membrane tobe measured is selected from the group consisting of the following:porous membrane such as microfiltration membrane, ultrafiltrationmembrane, nanofiltration membrane, and ion exchange membrane.

In one embodiment, the method of measuring the streaming potential Ē ofthe membrane uses a high impedance voltmeter to measure the potentialdifference across the membrane.

According to another embodiment of the invention, an apparatus 100 formeasuring a net charge density of a membrane is disclosed. The apparatus100 shown in FIG. 3 comprises a membrane permeation measurement module200, a pressure measurement module 300, a streaming potentialmeasurement module 400, a membrane resistance measurement module 500,and a control module 600. FIG. 4 shows a functional block diagramillustrating an apparatus 100′ for measuring a net charge density of amembrane according to another embodiment of the invention. Thedifference between the apparatus 100 and the apparatus 100′ is that theapparatus 100′ further comprises an electroosmotic flow measurementmodule 450. The pressure measurement module 300 measures the mechanicalpressure difference between the two surfaces of the membrane to bemeasured. The streaming potential measurement module 400 measures thestreaming potential of the membrane to be measured. The electroosmoticflow measurement module 450 measures the electroosmotic volumetric flowrate of the membrane. The membrane resistance measurement module 500measures the resistance of the membrane. The control module 600 controlsmeasurement procedures and collects data from each module to calculatethe net charge density of the membrane per unit volume. The controlmodule 600 can be for example a computer.

FIG. 5 shows a schematic diagram illustrating the connection of themembrane permeation measurement module 200, the pressure measurementmodule 300, and the streaming potential measurement module 400 shown inFIG. 3. FIG. 6 shows a schematic diagram illustrating the connection ofthe membrane permeation measurement module 200, the pressure measurementmodule 300, the streaming potential measurement module 400 and theelectroosmotic flow measurement module 450 shown in FIG. 4. The membranepermeation measurement module 200 comprises a chamber 210, a membrane230 to be measured, and a solution 240. Besides, the membrane permeationmeasurement module 200 can further comprise a temperature controller tocontrol the chamber 210 at a fixed temperature (for example, controllingthe chamber 210 at 25□); a pump, for transporting the liquid into thechamber; an electronic balance, for measuring a flow quantity of theliquid flowing through the membrane and outputting the flow quantity;and a power supply, electrically coupled to the two electrodes of themembrane permeation measurement module 200.

The pressure measurement module 300 comprise a pressure valve, forcontrolling and applying a pressure on the two surfaces of the membraneto generate a mechanical pressure difference ΔP between the two surfacesof the membrane; and a pressure sensor, for measuring the mechanicalpressure difference ΔP and outputting the mechanical pressure differenceΔP.

The streaming potential measurement module 400 comprises a highimpedance voltmeter, for measuring voltage between the two electrodeswhen the liquid passes through the membrane and outputting the voltage.

The electroosmotic flow measurement module 450 comprises a power supply,two electrodes of which are coupled to the two electrodes of themembrane permeation measurement module 200, and an electronic balancefor measuring the electroosmotic flow rate.

The pressure measurement module applies a mechanical pressure differenceΔP on the membrane to generate permeate flow and at the same time thestreaming potential measurement module measures the streaming potential.From the relation of the streaming potential and the mechanical pressuredifference, the net charge density of the membrane per unit volume canbe acquired. If additionally the electroosmotic flow measurement moduleapplies an electric field to generate electroosmotic flow to have themagnitude of the electroosmotic flow equal to the permeate flow butopposite in direction, the net charge density of the membrane per unitvolume can be acquired from the relation of the current and theelectroosmotic flow.

According to the above embodiment, the net charge density ρ_(E) of themembrane per unit volume can be acquired according to the relation ofthe mechanical pressure difference ΔP and the streaming potential Ē bythe equation (7): ρ_(E)=−(Ē/ΔP)*(μ∈k_(m)/K_(p)) where ∈k_(m) representsthe product of the porosity ∈ and average electrical conductivity k_(m)of the membrane, μ represents viscosity of the solution, and K_(p)represents permeability. In addition, the net charge density ρ_(E) ofthe membrane per unit volume can be acquired from the equation (9):ρ_(E)=−(Q_(p)/I_(a))*(μ∈k_(m)/K_(p)) where ∈k_(m) represents the productof the porosity ∈ and average electrical conductivity k_(m) of solutionin the membrane pore, μ represents viscosity of the solution, K_(p)represents permeability obtained from the permeate flow, I_(a)represents the current caused by the electric field, and Q_(p)represents the volumetric flow rate of the electroosmotic flow.

FIG. 7 shows a schematic diagram illustrating a membrane resistancemeasurement module 500 according to one embodiment of the invention. Themembrane resistance measurement module 500 comprises a membraneresistance measurement container 510, two electrode plates 521, 522, asolution, an AC power supply 530, and two voltmeters 541, 542. Theelectrode plates 521, 522 are disposed in the membrane electricresistance measurement container 510 and have a specific distancebetween the two electrode plates 521, 522. The solution is filled in themembrane resistance measurement container. The voltmeter 541 areconnected to the electrode plates 521, 522. One contact of the voltmeter542 is coupled to the AC power supply 530 and the other is coupled tothe electrode plate 522. The voltmeter 541, 542 measure voltages andcurrents. Under a specific voltage, the variation of currents betweenthe two electrodes is measured twice while the membrane is installed inbetween and is not installed and then the electric resistance of themembrane is calculated from the above relation of current variationbased on Ohm's law.

In addition, another embodiment of the invention provides an apparatusfor measuring electric resistance of a membrane by having the abovemembrane resistance measurement module become a stand-alone apparatus.

Moreover, another embodiment of the invention provides a method formeasuring electric resistance of a membrane, comprising: providing asolution; having the solution infiltrate the membrane; disposing themembrane between two electrodes and filling the solution between themembrane and each electrode; and measuring the relation of current andvoltage between the two electrodes and calculating the resistance of themembrane according to Ohm's law.

In conclusion, the invention discloses a method for measuring a netcharge density of a membrane and an apparatus thereof to utilize theapplied mechanical pressure difference and the streaming potential ofthe membrane or the applied electric field and the electroosmoticvolumetric flow rate of the electroosmotic flow to acquire the netcharge density inside the membrane so that the net charge density perunit volume can be measured effectively to solve the problem in theprior art.

According to the method for measuring electric resistance of a membraneand apparatus thereof, the resistance of a porous membrane such as amicrofiltration (MF), ultrafiltration (UF) or nanofiltration (NF)membrane is measured. Furthermore, if the porosity of the membrane isknown to be ∈ (for example, when a membrane has large pores, theporosity ∈ can be obtained from other methods), the average electricalconductivity k_(m) of solution in the membrane pore can be acquiredaccording to the method and apparatus for measuring electric resistanceof a membrane disclosed by the invention. On the other hand, if theaverage electrical conductivity k_(m) of the membrane is known, theporosity ∈ can be acquired according to the method and apparatus formeasuring electric resistance of a membrane disclosed by the invention.

Obviously many modifications and variations are possible in light of theabove teachings. It is therefore to be understood that within the scopeof the appended claims the present invention can be practiced otherwisethan as specifically described herein. Although specific embodimentshave been illustrated and described herein, it is obvious to thoseskilled in the art that many modifications of the present invention maybe made without departing from what is intended to be limited solely bythe appended claims.

What is claimed is:
 1. An apparatus for measuring a net charge densityof a membrane, comprising: a membrane permeation measurement module,comprising a chamber, two electrodes disposed in the chamber, a targetmembrane to be measured, and a solution, for measuring permeation ratecaused by a pressure difference ΔP between two surfaces of the targetmembrane and electroosmotic volumetric flow rate caused by an electricfield applying across the target membrane; a pressure measurementmodule, for measuring the mechanical pressure difference ΔP between thetwo surfaces of the target membrane; and a streaming potentialmeasurement module, for measuring the streaming potential Ē across thetarget membrane; and a control module, for controlling measurementprocedures and collecting data from each module to calculate the netcharge density ρ_(E) of the target membrane per unit volume according tothe relation of the mechanical pressure difference ΔP and the streamingpotential Ē, by the following equation (7):ρ_(E)=−(Ē/ΔP)*(μ∈k _(m) /K _(p))  (7) where ∈k_(m) represents theproduct of the porosity ∈ and average electrical conductivity k_(m) ofthe target membrane, μ represents viscosity of the solution, and K_(p)represents permeability; and wherein the product of the porosity ∈ andaverage electrical conductivity k_(m) of the target membrane is acquiredby measuring electric resistance of the target membrane.
 2. Theapparatus according to claim 1, further comprising: a membrane electricresistance measurement module, for measuring resistance of the targetmembrane.
 3. The apparatus according to claim 1, wherein the membranepermeation measurement module further comprises: a temperaturecontroller, for controlling the chamber at a fixed temperature; a pump,for transporting the solution into the chamber; an electronic balance,for measuring a flow quantity of the solution flowing through the targetmembrane and outputting the flow quantity; and a power supply,electrically coupled to the two electrodes of the membrane permeationmeasurement module.
 4. The apparatus according to claim 1, wherein thepressure measurement module comprises: a pressure valve, for controllingand applying a pressure on the two surfaces of the target membrane togenerate a mechanical pressure difference ΔP across the target membrane;and a pressure sensor, for measuring the mechanical pressure differenceΔP and outputting the mechanical pressure difference ΔP.
 5. Theapparatus according to claim 1, wherein the streaming potentialmeasurement module comprises: a high impedance voltmeter, for measuringvoltage between the two electrodes when the solution passes through thetarget membrane and outputting the voltage.
 6. The apparatus accordingto claim 1, wherein the membrane electric resistance measurement modulecomprises: a membrane resistance measurement container; two electrodeplates, disposed in the membrane resistance measurement container andhaving a specific distance between the two electrode plates; a solution,filled in the membrane resistance measurement container; an AC powersupply, for supplying power between the two electrode plates; twovoltmeters, one of which is electrically coupled to the two electrodeplates and the other of which has one end electrically coupled to the ACpower supply and has the other end electrically coupled to one of thetwo electrode plates to measure voltages and currents; wherein under aspecific voltage the variation of currents between the two electrodes ismeasured while the target membrane is installed in between or is notinstalled and then the resistance of the target membrane is calculatedfrom the above relation of current variation based on Ohm's law.
 7. Anapparatus for measuring resistance of a membrane, comprising: a membraneresistance measurement container; two plate-electrodes, disposed in themembrane resistance measurement cell and having a specific distancebetween the two electrode plates; a solution, filled in the membraneresistance measurement cell; an AC power supply, for supplying powerbetween the two electrode plates; two voltmeters, one of which iselectrically coupled to the two electrode plates and the other of whichhas one end electrically coupled to the AC power supply and has theother end electrically coupled to one of the two electrode plates tomeasure voltages and currents; and a control module, for controllingmeasurement procedures and collecting data from each module to calculatethe net charge density ρ_(E) of the target membrane per unit volumeaccording to the relation of the mechanical pressure difference ΔP andthe streaming potential Ē, by the following equation (7):ρ_(E)=−(Ē/ΔP)*(μ∈k _(m) /K _(p))  (7) where ∈k_(m) represents theproduct of the porosity ∈ and average electrical conductivity k_(m) ofthe target membrane, μ represents viscosity of the solution, and K_(p)represents permeability; and wherein the product of the porosity ∈ andaverage electrical conductivity k_(m) of the target membrane is acquiredby measuring electric resistance of the target membrane, and whereinunder a specific voltage the variation of currents between the twoelectrodes is measured while the target membrane is installed in betweenor is not installed and then the resistance of the target membrane iscalculated from the above relation of current variation based on Ohm'slaw.